While the USA does not have formal exit controls in the sense of a checkpoint, DHS is fully authorized to conduct exactly the same inspections or examinations as the case may be on individuals leaving the USA.

Here this is done on a randomized basis. But bags (carry-ons at this stage) are fully subject to search and CBP has LEO agents who, as the title denotes, have full Federal law enforcement authority. CBP can also conduct searches of checked luggage outbound.

As to TSA, the fact that an Officer does not himself have law enforcement authority does not mean that he can't report his own observations of violations of law to the appropriate law enforcement authority.